Mathematics
Mathematics, 24.02.2021 22:10, oofoofoof1

One-fourth the difference between 2/3 and 1/2.

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Prove (a) cosh2(x) āˆ’ sinh2(x) = 1 and (b) 1 āˆ’ tanh 2(x) = sech 2(x). solution (a) cosh2(x) āˆ’ sinh2(x) = ex + eāˆ’x 2 2 āˆ’ 2 = e2x + 2 + eāˆ’2x 4 āˆ’ = 4 = . (b) we start with the identity proved in part (a): cosh2(x) āˆ’ sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 āˆ’ sinh2(x) cosh2(x) = 1 or 1 āˆ’ tanh 2(x) = .
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